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Ant highway with energy loss (Posted on 2018-08-24) Difficulty: 5 of 5
An ant starts at the origin of the coordinate plane. The ant only has enough energy to walk for 10 units along either the x- or y-axis before stopping. These lines are the two ant highways.

However, if it goes off the highway, more energy is needed for the same distance. That is, the further the ant deviates, the greater the energy consumption, as represented by the factor 1+0.4d, where d is the distance to the nearest highway. For example, if the ant is 1 unit away from the nearest highway, it uses 1.4 times the energy on the highway to walk 1 meter.

What is the area of the set of points the ant can reach before getting tired and stopping?

No Solution Yet Submitted by Jer    
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re(2): heuristic computer solution | Comment 5 of 9 |
(In reply to re: heuristic computer solution by Jer)

Hmmm... I'm thinking that perhaps what's missing is a rounding of the concave cusp where the outer edges of the horizontal shape intersect the outer edges if the vertical shape that together make up the whole shape.


Also if this is the case, neglecting to consider rays once they go below the y=x line (and then go back above it) could be the cause of the defect, as these possibly cause the rounding of that concave cusp.

The trick then is not to count certain end points and their Riemann rectangles doubly--once from a ray dipping below y=x and once, farther in, from a ray not so dipping. I'll have to see about modifying my program.

  Posted by Charlie on 2018-08-25 12:07:58
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